Estimating rate- and state-friction parameters using a two-node stochastic model for aftershocks

Abstract

The well-known Omori, and modified Omori (Omori-Utsu), empirical formulae describe the decay in the rate of occurrence of aftershocks. Dieterich's rate- and state-dependent constitutive law for aftershock production produces a similar temporal formula with physically interpretable parameters, such as the shear stressing rates, the normal stress, and a fault constitutive parameter. This naturally leads to an interest in estimating these parameters from earthquake catalogs, which requires a simpler stochastic model. An alternative to the Epidemic Type Aftershock Sequence (ETAS) model is the two-node seismic transfer and release model, where one node represents the mainshock process, and a secondary node represents the aftershock zone. The aftershock decay rate in the two-node model equals that derived from Dieterich's rate- and state-dependent constitutive law, and the inclusion of aseismic slip in the aftershock zone allows for values of p > 1 in the best matching modified Omori law. The two-node model can be easily fitted to aftershock data, and has an application to aftershock stacking for estimating p-values. The equivalence between the rate- and state- and two-node aftershock rates forms a bridge between a formula derived from physical considerations and a phenomenological stochastic model. We show how this can be exploited, by identifying physical units for the parameters in the latter, to estimate the fault constitutive parameters, and the stressing rates, in Dieterich's formula through a best-fit inversion on real aftershock sequences. The procedure is illustrated using data from four Japanese earthquakes.